Prove Boolean Equation: XY+X(Y+Z)+Y(Y+Z) = Y+XZ
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Prove Boolean Equation: XY+X(Y+Z)+Y(Y+Z) = Y+XZ
Expert Solution
Step 1: Part A
We shall solve this problem using the TRUTH TABLE as shown below.
The truth table for the Left-hand side of the above Boolean expression is:
X | Y | Z | XY | XZ | YZ | XY+X(Y+Z)+Y(Y+Z) |
FALSE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE |
FALSE | FALSE | TRUE | FALSE | FALSE | FALSE | FALSE |
FALSE | TRUE | FALSE | FALSE | FALSE | FALSE | TRUE |
FALSE | TRUE | TRUE | FALSE | FALSE | TRUE | TRUE |
TRUE | FALSE | FALSE | FALSE | FALSE | FALSE | FALSE |
TRUE | FALSE | TRUE | FALSE | TRUE | FALSE | TRUE |
TRUE | TRUE | FALSE | TRUE | FALSE | FALSE | TRUE |
TRUE | TRUE | TRUE | TRUE | TRUE | TRUE | TRUE |
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